Here, a discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating kinks along the step edges. Model energetics and kinetics appropriately account for binding of adatoms at steps and kinks, distinct terrace and edge diffusion rates, and possible additional barriers for attachment to steps. Analysis of adatom attachment fluxes as well as limiting values of adatom densities at step edges for nonuniform deposition scenarios allows determination of both permeability and kinetic coefficients. Behavior of these quantities is assessed as a function of key system parameters including kink density, step attachment barriers, and the step edge diffusion rate.

Deposition on a vicinal surface with alternating rough and smooth steps is described by a solid-on-solid model with anisotropic interactions. Kinetic Monte Carlo (KMC) simulations of the model reveal step pairing in the absence of any additional step attachment barriers. We explore the description of this behavior within an analytic Burton-Cabrera-Frank (BCF)-type step dynamics treatment. Without attachment barriers, conventional kinetic coefficients for the rough and smooth steps are identical, as are the predicted step velocities for a vicinal surface with equal terrace widths. However, we determine refined kinetic coefficients from a two-dimensional discrete deposition-diffusion equation formalism which accounts for stepmore » structure. These coefficients are generally higher for rough steps than for smooth steps, reflecting a higher propensity for capture of diffusing terrace adatoms due to a higher kink density. Such refined coefficients also depend on the local environment of the step and can even become negative (corresponding to net detachment despite an excess adatom density) for a smooth step in close proximity to a rough step. Incorporation of these refined kinetic coefficients into a BCF-type step dynamics treatment recovers quantitatively the mesoscale step-pairing behavior observed in the KMC simulations.« less

Defining the conformational states of cytochrome P450 active sites is critical for the design of agents that minimize drug-drug interactions, the development of isoform-specific P450 inhibitors, and the engineering of novel oxidative catalysts. In this paper, we used two-dimensional 1H,15N HSQC chemical shift perturbation mapping of 15N-labeled Phe residues and x-ray crystallography to examine the ligand-dependent conformational dynamics of CYP119. Active site Phe residues were most affected by the binding of azole inhibitors and fatty acid substrates, in agreement with active site localization of the conformational changes. This was supported by crystallography, which revealed movement of the F-G loop withmore » various azoles. Nevertheless, the NMR chemical shift perturbations caused by azoles and substrates were distinguishable. The absence of significant chemical shift perturbations with several azoles revealed binding of ligands to an open conformation similar to that of the ligand-free state. In contrast, 4-phenylimidazole caused pronounced NMR changes involving Phe-87, Phe-144, and Phe-153 that support the closed conformation found in the crystal structure. The same closed conformation is observed by NMR and crystallography with a para-fluoro substituent on the 4-phenylimidazole, but a para-chloro or bromo substituent engendered a second closed conformation. An open conformation is thus favored in solution with many azole ligands, but para-substituted phenylimidazoles give rise to two closed conformations that depend on the size of the para-substituent. Finally, the results suggest that ligands selectively stabilize discrete cytochrome P450 conformational states.« less

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less